Marine seismic exploration is an extremely important tool for location of off-shore reserves. One known procedure for marine seismic exploration involves use of an ocean bottom cable as illustrated in prior art FIG. 1. Surveys using ocean bottom cables are typically employed in areas populated with numerous obstacles, such as drilling and production platforms. In this technique, several miles of bottom cables 11 (only one shown in the FIG. 1) are deployed along the sea floor 13 by vessel 15. Usually, multiple cables 11 are deployed in parallel, as shown in FIG. 2. The bottom cable 11 is provided with a plurality of sensor pairs 17 placed at regular intervals along the cable, each sensor pair 17 containing a pressure sensor (e.g., hydrophone) and particle velocity sensor (e.g., geophone). Acoustic energy is generated in the vicinity of the cable using an air gun array or a marine vibrator array 19. The source wavelet travels downward through the earth and is partially reflected by subsurface layers (formation 21 in FIG. 1) that present an acoustic impedance contrast. The primary reflected wavelet 23 travels upwardly from the subsurface layer, and the pressure waves generated by the upward-traveling reflection are detected by the sensor pairs 17.
Seismic exploration using ocean bottom cables is complicated by secondary waves such as wave 25, known as "ghosts," that are received by the sensors pairs 17 as downward-traveling reflections after reflecting off the air/water boundary at the surface 29. The air/water boundary is an efficient reflector, and thus the ghosts are significant in amplitude and are difficult to differentiate from the primary waves. These ghosts adversely affect the data obtained during the exploration by attenuating certain frequencies. In addition, when the water depth is large, the spectral ghost notches fall in the seismic frequency band and drastically affect the seismic resolution. Resolution is further complicated by multiple reflection waves and water layer reverberations such as wave 27.
The purpose of using both hydrophones and geophones in the ocean bottom cable is to capitalize on the differences between these two types of sensors to attenuate the downgoing waves which include the ghosts and the water layer reverberations. Their responses to the primary reflections are in phase, but are 180.degree. out of phase to the ghosts and to the reverberations.
FIG. 3a illustrates amplitude versus time hydrophone response at the water bottom. For the hydrophone, at time t.sub.1 (the primary wave), the hydrophone response is defined as T. At time t.sub.2 (the first water layer reverberation), the hydrophone response is -(1+r)T; at time t.sub.3 (the second reverberation) it is r(1+r)T; and at time t.sub.4 (the third reverberation), it is -r.sup.2 (1+r)T, where r is between 0 and 1 and is the water bottom reflectivity at each receiver position. Additional reverberations continue to decrease in amplitude.
The geophone amplitude versus time response is shown in FIG. 3b. The amplitude at t.sub.1 is MT, where M is a sensitivity scaling factor that depends upon the particular type of sensors used. At time t.sub.2, the geophone response is (1-r)MT. At time t.sub.3, the response is -r(1-r)MT, and at time t.sub.4 is r.sup.2 (1-r)MT.
It is apparent from FIGS. 3a and 3b that while the primary geophone and hydrophone responses are in phase, the responses to the water layer reverberations are 180.degree. out of phase. Thus, the attenuation of the reverberations can be achieved by adding the hydrophone and the geophone signals together after the signals have been suitably scaled. Theoretically, the scale factor S=(1+r)/(1-r), where r is the water bottom reflectivity, should be applied to the geophone data. Determination of the water bottom reflectivity coefficient r depends upon the acoustic impedance of the bottom material. Thus, the scale factor S can vary among different sensor pair locations on the same cable.
There are several known methods for deriving the scaling factors for geophone signals. U.S. Pat. No. 5,235,554 describes a method where a calibration survey is used to estimate the water bottom reflection coefficient. In such a calibration survey, a low energy source is fired over each sensor pairs and the scale is determined from the ratio of the peaks of the first arrivals of the hydrophone and geophone signals. Collection of this survey data requires additional time and cost over and above the data acquisition phase of the survey. U.S. Pat. No. 5,396,472 describes a method to derive the water bottom reflection coefficient that eliminates the need for a separate calibration survey, but involves complex mathematics including summing the pressure and velocity signals, multiplying the results by the inverse Bachus operator, and then solving for the water bottom reflectivity r using an optimization algorithm. U.S. Pat. No. 5,365,492 describes a method wherein the hydrophone signal is used first to adaptively remove noise from the geophone signal, and then the cleaned geophone signals are scaled by a scaling factor and added to the hydrophone signals. The resulting signal is then auto-correlated and the relative amplitude of the first auto-correlation's function-side lobe is measured. The optimum scale factor for the geophone data is then found by optimizing the value of the scale factor with respect to the first side-lobe amplitude of the auto-correlation.